Non-Archimedean techniques and dynamical degenerations

2024/06/22 by Favre, Charles, Gong, Chen · 3 citations
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.15892

Abstract

We develop non-Archimedean techniques to analyze the degeneration of a sequence of rational maps of the complex projective line. We provide an alternative to Luo's method which was based on ultra-limits of the hyperbolic 3-space. We build hybrid spaces using Berkovich theory which enable us to prove the convergence of equilibrium measures, and to determine the asymptotics of Lyapunov exponents.

Cited by

• Action de groupe sur la compactification hybride
• Multiplier scales of a sequence of rational maps
• On the Number of Small Points for Rational Maps

Related

• The intrinsic reductions and the intrinsic depths in non-archimedean dynamics
• Degenerations of Complex Dynamical Systems
• A dynamical system over a non-archimedean field
• Degeneration of endomorphisms of the complex projective space in the\n hybrid space
• Arbitrary large number of non trivial rescaling limits